Related papers: Band Topology or Geometry?

Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index.…

The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…

In commonly employed models for 2D topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to…

A band with a nonzero Chern number cannot be fully localized by weak disorder. There must remain at least one extended state, which ``carries the Chern number.'' Here we show that a trivial band can behave in a similar way. Instead of fully…

Two-dimensional (2D) bismuth (Bi) layer, known as bismuthene, exhibits $Z2$ topological bulk states due to large spin-orbit coupling that inverts the bands. Using the tight-binding method, we calculate the band structure of buckled…

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for…

Topological order can be found in a wide range of physical systems, from crystalline solids, photonic meta-materials and even atmospheric waves to optomechanic, acoustic and atomic systems. Topological systems are a robust foundation for…

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…

Topological insulators are transformative quantum solids with immune-to-disorder metallic surface states having Dirac band structure. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to…

Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely…

The interplay between band topology and magnetic order plays a key role in quantum states of matter. MnBi2Te4, a van der Waals magnet, has recently emerged as an exciting platform for exploring Chern insulator physics. Its layered…

We study the relationship between the shape of the electronic band structure and the thermoelectric properties. In order to study the band shape dependence of the thermoelectric properties generally, we first adopt models with band…

How do we uniquely identify a quantum phase, given its ground state wave-function? This is a key question for many body theory especially when we consider phases like topological insulators, that share the same symmetry but differ at the…

Motivated by the abundance of symmetry breaking states in magic-angle twisted bilayer graphene and other two-dimensional materials, we study superconducting (SC) and charge orders in two-dimensional topological flat bands in the strong…

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the…

Spin-orbit coupled materials have attracted revived prominent research interest as of late, especially due their direct connection with topological notions. Arguably, a hallmark of this pursuit is formed by the concept of the topological…

This paper is a survey of the $\mathbb{Z}_2$-valued invariant of topological insulators used in condensed matter physics. The $\mathbb{Z}$-valued topological invariant, which was originally called the TKNN invariant in physics, has now been…

Recent advancements in the field of topological band theory have significantly contributed to our understanding of intriguing topological phenomena observed in various classical and quantum systems, encompassing both wave and dissipative…

Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…